• Cite Icon59
  • https://doi.org/10.1109/2945.489383Copy DOI Icon

Volume-preserving free-form solids

Show More
  • Abstract
  • Literature Map
  • References
  • Citations
  • Similar Papers
Abstract

Some important trends in geometric modeling are the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models, by using free-form objects in addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper, we integrate all of these requirements into a single geometric primitive by endowing the tri-variate tensor-product free-form solid with several important physical properties, including volume and internal deformation energy. Volume preservation is of benefit in several application areas of geometric modeling, including computer animation, industrial design and mechanical engineering. However, previous physics-based methods, which have usually used some form of "energy", have neglected the issue of volume (or area) preservation. We present a novel method for modeling an object composed of several tensor-product solids while preserving the desired volume of each primitive and ensuring high-order continuity constraints between the primitives. The method utilizes the Uzawa algorithm for non-linear optimization, with objective functions based on deformation energy or least squares. We show how the algorithm can be used in an interactive environment by relaxing exactness requirements while the user interactively manipulates free-form solid primitives. On current workstations, the algorithm runs in real-time for tri-quadratic volumes and close to real-time for tri-cubic volumes.

Similar Papers
  • Book Chapter
  • Citations5

Strengthening the Interaction of Art and Science Through Rubric-Based Evaluation Models: The Final Degree Project of the Dual Degree of Engineering in Industrial Design and Mechanical Engineering

  • Sep 21, 2018
  • R Díaz-Obregón +3
  • Research Article
  • Citations4

Computer graphics and computer aided design in mechanical engineering at the University of Minnesota

  • Jan 01, 1981
  • Computers & Education
  • Donald R Riley +1
  • Research Article

Effects of elastic energy on the spinodal decomposition in InAlGaN materials

  • Mar 14, 2011
  • physica status solidi c
  • Salvador F Diaz Albarran +1
  • Book Chapter
  • Citations1

Mapping Design Curriculum in Schools of Design and Schools of Engineering: Where do the Twains Meet?

  • Jan 01, 2013
  • Peer M Sathikh
  • Research Article

10th Anniversary Special Issue: From Fringe to Mainstream—We Have Come a Long Way

  • Jun 01, 2011
  • Journal of Computing and Information Science in Engineering
  • Jami J Shah
  • Research Article
  • Citations21

Interdisciplinary By Design

  • Sep 01, 2008
  • Mechanical Engineering
  • Tim Simpson +2
  • Dissertation

Modeling and processing of physically based dynamic t-splines

  • Jan 01, 2013
  • Yuewen Ma
  • Research Article
  • Citations1

Estimation of Neutron Yield from Individual Fragment in Medium-Excitation Fission

  • Jul 01, 1979
  • Journal of Nuclear Science and Technology
  • Hisao Yamamoto +4
  • Research Article
  • Citations2

Switching Functions Based Geometric Modeling Language and its Application to Numerical Control Program Verification

  • Jan 01, 1987
  • CIRP Annals - Manufacturing Technology
  • M Shpitalni +2
  • Conference Article
  • Citations17

Information Sharing Within a Distributed, Collaborative Design Process: A Case Study

  • Sep 09, 2001
  • Steven P Macgregor +2
  • Conference Article
  • Citations1

Solid Model in Geometric Modelling System : HICAD

  • Jun 27, 1983
  • Shinji Tokumasu +4
  • Research Article
  • Citations1

Boolean operations based on the planar polyhedral representation

  • Jan 01, 1988
  • Computers & Graphics
  • J Flaquer
  • Research Article

Boolean operations based on the planar polyhedral representation: Comput. & Graph. Vol 12 No 1 (1988) pp 59–64

  • Sep 01, 1988
  • Computer-Aided Design
  • J Flaquer +1
  • Research Article
  • Citations5

Virtual reality (VR) technologies in education of industrial design

  • Feb 19, 2016
  • New Trends and Issues Proceedings on Humanities and Social Sciences
  • Bulent Yilmaz +1
  • Research Article
  • Citations4

Virtual reality (VR) technologies in education of industrial design

  • Feb 19, 2016
  • Global Journal on Humanities and Social Sciences
  • Bülent Yılmaz +1
Cactus Communications logo

Copyright 2026 Cactus Communications. All rights reserved.